Piano strings are audibly inharmonic due to stiffness
[212,211]. General stiff-string modeling
was introduced in §6.9. In this section, we discuss
further details specific to piano strings.

The main effect of string stiffness is to stretch the partial
overtone series, so that piano tones are not precisely harmonic
[145]. As a result, piano tuners typically
stretch the tuning of the piano slightly. For example, the total
amount of tuning stretch from the lowest to highest note has been
measured to be approximately 35 cents on a Kurzweil PC88, 45 cents on
a Steinway Model M, and 60 cents on a Steinway Model D.10.18